I am using the N-Channel 40-V (D-S) MOSFET Si4154DY From Vishay Siliconix; the datasheet confuse me, I need to now what will be the continuous current (DC current, not pulse current) allowed. can any one help me to find this in the datasheet? I know that this will depend on the ambient temperature, The Gate-to-Source Voltage... but I was not able to find that in the datasheet.
It depends on your thermal parameters, your ambient temperature, and your max allowed die temperature.
The datasheet shows a plot of power derating vs ambient temperature, that's probably the most useful one if you have no heatsinking. Use that to find your max power dissipation, then calculate ID using P=I^2*Rds. For example if your Ta=25C, and Rds=3.3mohm, then Pmax is about 1.5W and IDmax is 21.3A.